MATH
222 Test 2 Name____________________
Instructions:
Answer all the questions on the paper provided and show all your work. You may use a calculator on all questions.
1. Plot the points given in polar coordinates in
the graphical region below: (6)
A
(3,p/4), B (2, 7p/6), C (-2, 11p/4)
2. Find the area of the region enclosed by the
curve r = 2cos(3q). (10)
3. Find the equation of the line tangent to the
parametric curve at the point corresponding to t = 2 when the curve is given by
x(t) = 2t2, y(t) = t3-2. (8)
4. Find three different sets of polar
coordinates for the point given in x-y coordinates by 
. One of the sets of
polar coordinates should have a negative value for r. (6)
5. Transform the equation 
into a standard form
for a conic section. Identify the curve and find all its relevant parts (foci
etc.) (14)
6. Expand
in partial fractions
but do not evaluate the resulting integral.
Find all necessary coefficients. (12)
7. Evaluate 
including all
necessary limits. (16)
8. Expand 
into a partial
fraction expansion, but do not find the value of the coefficients. (8)
9. Find the equation in standard form of the
parabola with its focus at (1,6) and its directrix
given by x = -5. (10)
10. Find the length of the curve given by 
. (8)